It can detect power outages. There is a extra power port to sense outages. The profilux itself needs to be powered via UPS for that to work of course.
You can configure how your tank should react to a power outage.
I don't know if it can notify you as I have a 3rd gen profilux only. But I would very much expect that. Just can't confirm it.
For a P4 it will notify you but it through your network. So if your router is down due to the power outage you would not receive the notification.

. I did the Captcha thing (though perhaps not in the order that is mentioned in other posts) and the "less secure Apps" is also checked (though I really hate to do it). When I click on "Test" absolutely nothing happens. No error message, no email,... nothing. I did set it up using the P4 wifi connection, not the USB...